Babbel was shown a straight red for his angry outburst in the midst of the VAR controversy during the weekend's Sydney Derby.
He threw his jacket to the ground, kicked sideline hoardings and reportedly swore at officials as referee Chris Beath controversially overturned a Wanderers goal on the hour mark.
He was shown a red card - the first to a head coach in the A-League since the system was introduced - and sent to the SCG's stands to watch the game end in a 2-0 victory for Sydney FC.
Today the FFA's Match Review Panel upheld the red card and suspended Babbel for one game, the minimum allowed for a straight red.
A statement from the FFA added: "The MRP determined that Babbel had committed the offence of use of offensive, insulting or abusive language and/or gestures against a Match Official. The MRP confirmed that Babbel will serve a suspension of one match, the minimum sanction for the offence."